Question

The snake population in a swamp Is 1056. The population of the snakes is increasing by a factor of 28% each year.

Answer 1

a. Model the situation with an exponential function.
 The exponential function that models the problem in this case is:
 y = 1056 (1.28) ^ t
 Where,
 t: number of years

 b. Find how many alligators there will be in 8 years.
 For 8 years we must replace the value of t = 8 in the written equation.
 We have then:
 y = 1056 (1.28) ^ 8
 y = 7609.28193
 Nearest whole integer:
 y = 7609

 c. How many years will it take for the population to become 3000?

 For this we should almost replace y = 3000 in the equation of part A.
 We have then:
 3000 = 1056 (1.28) ^ t
 From here, we clear t:
 (1.28) ^ t = (3000) / (1056)
 We apply logarithm to both sides:
 log1.28 ((1.28) ^ t) = log1.28 ((3000) / (1056))
 t = log1.28 ((3000) / (1056))
 t = 4.229619111 years.